Submit: 1937 Solved: 1121
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Description
在N行M列的棋盘上，放若干个炮可以是0个，使得没有任何一个炮可以攻击另一个炮。 请问有多少种放置方法，中国像棋中炮的行走方式大家应该很清楚吧.
Input
一行包含两个整数N，M，中间用空格分开.
Output
输出所有的方案数，由于值比较大，输出其mod 9999973
Sample Input
1 3
Sample Output
7
HINT
除了在3个格子中都放满炮的的情况外，其它的都可以.
100%的数据中N,M不超过100
50%的数据中，N,M至少有一个数不超过8
30%的数据中，N,M均不超过6
Source
f[i][j][k]表示截止到第i行为止，在所有的列中有一个炮的有j列，有2个炮的有k列。
推想出以下6种状态：
1：在下一行什么也不放： f[i+1][j][k]=f[i+1][j][k]+f[i][j][k];
2：在下一行中找一个0个炮的列去放一个炮： f[i+1][j+1][k]=f[i+1][j+1][k]+f[i][j][k]*(m-j-k);
3：在下一行中找一个1个炮的列去放一个炮： f[i+1][j-1][k+1]=f[i+1][j-1][k+1]+f[i][j][k]*j;
4：在下一行中找两个0个炮的列去分别放一个炮： f[i+1][j+2][k]=f[i+1][j+2][k]+f[i][j][k]*(m-j-k)*(m-j-k-1)/2;
（这里运用了组合数公式，因为有m-j-k个0个炮的列，任选两个进行组合，一共有C2m-j-k种放法，化简开来就是有(m-j-k)*(m-j-k-1)/2种）
5：在下一行中找一个0个炮的列和一个1个炮的列分别去放一个炮： f[i+1][j][k+1]=f[i+1][j][k+1]+f[i][j][k]*(m-j-k)*j;
6：在下一行中找两个1个炮的列去分别放一个炮： f[i+1][j-2][k+2]=f[i+1][j-2][k+2]+f[i][j][k]*j*(j-1)/2;
最后的ans是所有的f[n]加起来： ans=ans+f[n][j][k];
(copy(原地址))
存一下考场的无敌做法
O(1)的 (只可惜只有10分。。没弄全);
#include <cstdio> #define N 105 int n,m; long long ans[N][N]={{2,4,7,11,16,22,29,37,46,56,67,79,92,106,121,137,154,172,191,211,232,254,277,301,326,352,379,407,436,466,497,529,562,596,631,667,704,742,781,821,862,904,947,991,1036,1082,1129,1177,1226,1276,1327,1379,1432,1486,1541,1597,1654,1712,1771,1831,1892,1954,2017,2081,2146,2212,2279,2347,2416,2486,2557,2629,2702,2776,2851,2927,3004,3082,3161,3241,3322,3404,3487,3571,3656,3742,3829,3917,4006,4096,4187,4279,4372,4466,4561,4657,4754,4852,4951,5051}, {4,16,49,121,256,484,841,1369,2116,3136,4489,6241,8464,11236,14641,18769,23716,29584,36481,44521,53824,64516,76729,90601,106276,123904,143641,165649,190096,217156,247009,279841,315844,355216,398161,444889,495616,550564,609961,674041,743044,817216,896809,982081,73313,170741,274658,385346,503093,628193,760946,901658,50658,208230,374715,550443,735750,930978,136492,352612,579715,818167,68357,330629,605384,893012,193926,508494,837141,180298,538351,911743,300923,706295,128337,567465,24169,498877,992074,504251,35871,587403,159373,752245,366557,2802,661479,343144,48308,777488,531258,310147,114707,945479,803061,688006,600890,542295,512809,513026}, {7,49,265,1081,3481,9367,22009,46585,90811,165661,286177,472369,750205,152708,721058,505971,568930,983693,837823,234274,293101,153311,974685,939843,256229,158288,909750,805987,176375,386831,842474,990291,321927,376531,743794,66992,46068,440957,74899,837791,689816,664924,874590,511594,853840,268401,215467,252570,38780,339008,28467,97104,654241,933255,296331,239288,396597,546387,615575,685086,995163,950784,127135,275156,327296,403205,815601,76244,901864,220451,177278,141337,711661,723855,256615,638388,454190,552361,51563,347732,121273,344175,287369,528057,957216,787158,559146,151168,785733,37876,843015,505238,705323,509137,375938,166869,153491,26440,904123,341623}, {11,121,1081,7343,37441,149311,490631,386798,481594,948300,791333,261052,407035,797530,435235,902184,769206,307434,542456,693880,45571,294508,428797,187488,157840,567960,835262,933729,645566,765216,326401,925081,214237,648156,557419,637191,934918,425427,264132,811756,526193,819722,982645,276380,301968,752473,659951,250473,523173,671761,469342,740140,44161,703094,298898,778091,298416,955923,534131,418366,821928,472478,909845,549228,665659,458878,359577,741034,202389,592283,944526,499334,986705,350990,97725,447126,480438,468189,571971,113720,609004,763603,634692,161002,268463,760591,205214,31703,55649,649971,784402,157497,648048,315345,179783,18583,413218,288131,182495,499642}, {16,256,3481,37441,304186,859943,871377,590219,851614,245091,244338,627109,581314,93002,658598,171376,113529,55332,32550,758625,940712,322404,584832,14366,2811,99582,595755,603196,409442,655560,712171,632174,350925,498540,398696,666520,399133,388398,191236,380358,982361,102943,154637,54738,361530,681870,923061,192356,480403,814989,450456,981516,149704,659846,658038,751528,692301,209526,77505,457424,966666,922446,890094,154150,135418,213691,995859,907817,197445,130241,450719,185772,694160,632430,324629,6198,672829,917877,299321,553835,483642,695017,680169,118178,840927,779016,483467,626828,332995,383981,416894,268177,759336,561453,438201,263165,848846,926901,693804,298080}, {22,484,9367,149311,859943,526101,922457,947915,678888,646926,193281,916181,626250,241339,912723,933581,10257,945986,147659,339019,924184,298871,489382,446044,456409,979197,893106,13466,689572,404781,205998,219705,760404,953892,262717,718352,441411,564069,830759,770851,685432,967924,97606,514554,394540,846226,359234,376737,912903,243839,224063,842311,611060,408456,807853,799097,383714,748745,691095,425303,746124,232840,378984,400176,274497,124843,218089,17054,271602,963467,891903,135112,823540,326058,705818,180158,229592,234400,209954,846868,941284,37491,105678,24732,979003,302667,236612,143262,290187,891864,881397,219434,421700,508064,461223,341126,815654,485878,995956,546151}, {29,841,22009,490631,871377,922457,243963,250961,17941,487804,127548,597181,548897,271723,176185,98747,284236,885731,201236,375688,830703,499876,433898,430691,692079,484018,414614,900580,24207,631740,102471,180521,74134,187068,600541,215301,255117,358907,544939,197494,301386,901619,82209,798298,520662,537979,294406,144716,374741,146770,869879,957912,972028,917052,713264,887520,805322,421830,637644,205054,610758,387437,590215,285711,755016,987647,199907,120406,645883,617621,760663,598697,437452,499867,184939,645657,911391,533943,705968,978988,425041,825682,776324,139806,229168,781851,878133,154647,24176,602661,414181,513767,107734,464794,102254,241259,554410,505187,93837,703782}, {37,1369,46585,386798,590219,947915,250961,341999,620104,456808,49812,44529,926241,66306,159867,279092,559843,459933,411631,330272,313146,57216,775367,827872,141052,746587,483124,616836,887635,389506,350674,548345,645088,401772,683773,132971,363536,414852,414250,940880,120252,313222,703966,528956,929468,307097,26346,756827,148180,329418,37277,865657,570603,989565,613235,624856,990384,765081,882662,904407,736845,936829,951387,71373,828148,295778,90800,772491,74522,319028,347997,728147,973880,576106,221759,158549,604199,528596,475540,524529,967798,585473,715517,442455,737849,755938,385077,14391,585638,458185,586475,486545,374221,153184,121673,595645,74496,594415,159574,258983}, {46,2116,90811,481594,851614,678888,17941,620104,740488,50892,388992,719883,94772,490139,7074,231793,908728,817178,255794,143660,274772,220184,268530,932846,658984,44650,631494,703852,410906,618456,639217,116886,31351,822291,861522,436839,925516,921777,371281,674407,686173,22726,73878,57955,510361,877498,597230,45676,999791,155578,102550,181780,36975,1305,780112,786826,858666,628365,603502,517297,172879,716633,127429,340538,521577,153394,807294,132939,248596,307132,759570,930694,19684,27986,297860,638595,47289,125688,825137,253600,855169,626292,578322,997354,260106,887644,595394,799066,345633,159816,827694,436124,881609,755781,102467,530626,832136,828522,595312,864981}, {56,3136,165661,948300,245091,646926,487804,456808,50892,660595,823364,675437,741063,745960,794860,20093,711519,257174,891612,580212,566622,819486,196850,240312,894522,341501,876343,569433,882648,614615,547745,995832,387487,834988,681521,129207,784714,960202,348209,277062,863009,714950,707241,607578,994098,635073,277054,922749,702252,589677,724744,853078,933584,595788,942070,134700,755345,118459,440699,952293,2164,43487,864498,896628,740128,859022,424925,125181,430102,374371,519568,596534,188254,101631,648220,675825,807337,638347,662887,130257,631405,813671,976873,580823,135209,752415,462412,366429,494339,95361,827468,708527,938971,564449,862501,962208,441299,920913,978561,597297}, {67,4489,286177,791333,244338,193281,127548,49812,388992,823364,196319,750779,26750,132492,3752,573787,845285,343915,788033,852835,726066,951679,193918,313468,163059,685374,75251,763819,223905,393500,129153,134431,537176,719237,662018,474460,511137,91869,636697,510399,835356,530112,375505,241691,973755,669263,970497,44525,68173,453876,522605,217074,335707,299324,337270,377673,734370,220224,248586,551878,95076,867239,479551,786780,181278,752496,200174,811162,237284,16595,535308,126738,348392,508904,970907,247989,611478,209018,489157,293167,302587,850223,951324,739928,736319,43013,836858,338530,765570,840142,537547,471064,270096,778899,920969,270910,423150,437050,679102,997712}, {79,6241,472369,261052,627109,916181,597181,44529,719883,675437,750779,329938,868852,225798,898745,742711,235348,904213,224114,13195,15267,441261,617783,88218,938415,922003,47645,707765,350161,843418,211278,188247,254514,105776,480802,388832,337589,744334,991092,80411,79541,684864,250006,520913,6823,126665,858521,879633,251929,959543,97039,501235,664125,921896,115443,655671,483970,853865,588080,489604,852587,575357,566887,877163,786447,368447,620594,219444,372568,203181,10459,568145,363453,318242,333264,248900,305152,426646,858157,350774,737074,578807,968015,689468,682245,459300,612501,838299,134934,604743,432684,360664,461191,951645,255393,737271,336880,217218,889463,145071}, {92,8464,750205,407035,581314,626250,548897,926241,94772,741063,26750,868852,507550,192353,139653,279062,524633,114688,305865,249793,873922,345908,44465,903340,776542,587043,170893,485413,696830,706754,175620,161157,299529,712103,425465,667849,813960,39571,617551,136245,346054,542125,256808,640761,347528,450781,61298,487984,628007,605601,92557,782424,677984,882578,71905,766050,207842,793955,589912,107323,818436,297202,632182,183562,924264,280002,350067,292929,468169,554251,6619,61287,146771,812672,887469,600277,743604,179827,90773,620498,205891,292421,831259,811787,980629,996386,23488,519262,465860,105068,167129,849812,493900,264910,49112,506821,867290,213275,232736,979676}, {106,11236,152708,797530,93002,241339,271723,66306,490139,745960,132492,225798,192353,884008,808299,514046,912390,850562,166898,420316,90297,905603,417299,742296,958825,63750,654966,581229,784442,9781,955652,112092,540836,85738,690084,427648,757916,891079,711261,990461,101413,567318,600273,11655,602883,224298,645028,174097,987311,60050,648779,735556,705663,713780,569599,488174,91947,507475,805295,909445,848033,153653,490690,206077,662089,319044,434647,487604,632524,486955,99421,761259,555675,352854,532032,617898,765818,934798,332491,754143,944289,536793,820625,429250,223968,541894,780688,116044,685799,781262,112286,924965,38585,342613,641936,26437,468019,558425,672899,40793}, {121,14641,721058,435235,658598,912723,176185,159867,7074,794860,3752,898745,139653,808299,534510,216116,665996,365177,394605,24630,439792,865038,480301,806440,786630,469703,306958,924358,77267,647520,466100,753416,446279,933883,128947,140955,822643,455341,696563,602348,261602,505355,26328,672334,355711,210541,68653,896052,855526,635322,52217,370725,641090,11343,757093,722147,544408,257179,392757,838749,354920,555653,415418,341536,334733,752284,474983,660433,732436,94442,821104,807541,9097,807648,752981,7397,766934,138661,719711,128184,46388,244932,987174,873629,317427,759812,383090,86255,213030,490300,913847,728981,684737,339209,867361,327022,285856,76079,709593,252208}, {137,18769,505971,902184,171376,933581,98747,279092,231793,20093,573787,742711,279062,514046,216116,514741,437307,691932,332836,442690,191586,764107,637714,460079,954550,376528,462351,691777,871221,529834,7186,93198,113181,489742,537861,905764,401921,205198,996600,207291,763089,376740,708640,847183,962068,168330,987357,619288,897542,13655,812868,155481,674693,562815,733597,811888,55092,156684,943357,552476,36338,852133,681058,296075,651860,106175,912249,838993,99050,585765,346636,225808,43448,348359,972124,850510,400728,501507,662832,372688,119872,961644,794543,890949,673598,993672,909472,415212,687030,922853,901220,942705,423189,230122,396257,775731,329258,147578,524213,246107}, {154,23716,568930,769206,113529,10257,284236,559843,908728,711519,845285,235348,524633,912390,665996,437307,180367,823643,673586,603348,421325,391599,275091,800142,202169,523450,44824,519223,283170,481390,275319,915329,607964,250909,132083,674731,818455,366093,749492,84371,250775,664962,652944,73264,501775,320579,293247,431565,272666,80797,468974,250738,770780,185436,21511,236557,518686,968726,996459,720630,277034,627077,70951,739192,201262,593927,322081,235675,314235,447057,148108,982728,979473,193801,638788,594588,473512,637610,13021,814143,787596,279164,246232,735477,821909,837652,553346,793753,221078,386784,211998,752620,690207,228862,306592,757376,389028,92213,197279,915468}, {172,29584,983693,307434,55332,945986,885731,459933,817178,257174,343915,904213,114688,850562,365177,691932,823643,55815,927883,138107,904440,591257,492533,449142,342169,845244,751377,474047,451535,270085,411652,440515,680134,970071,356727,142867,785471,526519,370335,486930,98116,99151,807677,744264,669081,449109,614697,631840,239560,674399,103631,839692,660055,546854,762028,252106,856488,29836,523305,252504,5773,642406,495753,904303,65581,260471,963867,847933,736530,161827,30196,813138,555658,117274,745903,357464,7421,573220,506563,963432,743290,405168,494967,137882,146355,822152,465205,392608,544692,624636,236810,535885,872886,201380,758234,725203,994170,970804,465089,282723}, 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{3322,35871,121273,609004,483642,941284,425041,967798,855169,631405,302587,737074,205891,944289,46388,119872,787596,743290,981393,434988,69831,213435,532150,856516,483880,334161,717433,633208,301306,931564,477322,925745,916005,818287,658661,115459,378496,435044,348474,871847,403038,665814,725673,903596,56315,177639,262835,523917,960715,572613,285305,298508,497859,103608,565077,854407,133728,825087,904840,719229,194922,608017,25130,298196,651522,186230,272022,163463,473473,59332,493850,674309,571238,840883,784286,857312,904734,415086,331259,757429,601619,630992,402905,292112,968015,887711,898429,556635,327437,601830,424464,655734,478159,203458,870638,517248,143342,900013,386229,534870}, {3404,587403,344175,763603,695017,37491,825682,585473,626292,813671,850223,578807,292421,536793,244932,961644,279164,405168,271961,814590,467889,438739,646070,186339,701599,324096,831603,158632,199110,591295,355421,405713,341153,626198,263446,569720,781825,8322,162816,87998,621392,496841,922096,165869,180446,58348,377605,496635,842039,542872,221181,891159,79712,31877,364631,290927,596480,75410,538459,54843,126052,293834,669755,880256,112849,334116,472302,579389,452703,54207,882634,221904,796300,519939,695702,506193,187638,291049,922901,371380,630992,186476,851704,586979,725900,71387,785532,860515,805234,563586,888404,416867,617498,160176,466173,917168,145673,904011,527816,562201}, {3487,159373,287369,634692,680169,105678,776324,715517,578322,976873,951324,968015,831259,820625,987174,794543,246232,494967,768474,194793,451752,557211,392796,507706,498263,919574,269651,186024,620847,511298,779411,822826,974623,55456,976155,381128,813782,590407,10863,734055,84856,984784,559077,358900,957996,776304,481749,624255,176046,401327,384639,410783,945418,340729,895002,322190,933879,294982,94633,578936,121330,782869,191448,330353,604991,421876,313038,16251,489260,13159,825931,878056,130312,593451,692533,602062,591722,388897,859385,906562,402905,851704,521291,898197,551106,798656,94002,386364,658121,819037,69166,856228,193205,794345,613144,769273,77651,396016,539473,771638}, {3571,752245,528057,161002,118178,24732,139806,442455,997354,580823,739928,689468,811787,429250,873629,890949,735477,137882,434849,89987,133081,170484,288594,500218,35584,702841,780639,517291,734307,655006,176405,899256,657781,136596,492103,340802,115287,232225,658093,955120,263455,938045,307470,674910,829739,450197,187862,113440,633783,319326,47104,994809,534659,648541,955972,159779,11503,568506,330602,852800,434115,923996,884795,441149,595417,341981,271037,539394,80792,306251,459908,660840,701627,827984,688733,852772,748655,537884,926147,572291,292112,586979,898197,69629,162143,928065,646900,587170,869528,659665,979845,389959,791229}}; int main() { freopen("B.in","r",stdin); freopen("B.out","w",stdout); scanf("%d%d",&n,&m); printf("%I64d",ans[n-1][m-1]); return 0; fclose(stdin); fclose(stdout); }
#include<cstring> #include<cstdio> #define N 110 #define Mod 9999973 typedef long long LL; int n,m,i,j,k; LL f[N][N][N]; int main() { scanf("%d%d",&n,&m); f[0][0][0]=1; for(int i=0;i<n;++i) for(int j=0;j<=m;++j) for(int k=0;k<=m-j;++k) if(f[i][j][k]) { f[i+1][j][k]=(f[i+1][j][k]+f[i][j][k])%Mod; f[i+1][j+1][k]=(f[i+1][j+1][k]+f[i][j][k]*(m-j-k))%Mod; if(j>=1) f[i+1][j-1][k+1]=(f[i+1][j-1][k+1]+f[i][j][k]*j)%Mod; if(m-j-k>=2) f[i+1][j+2][k]=(f[i+1][j+2][k]+f[i][j][k]*((m-j-k)*(m-j-k-1)/2))%Mod; if(j>=1&&m-j-k>=1) f[i+1][j][k+1]=(f[i+1][j][k+1]+f[i][j][k]*(j*(m-j-k)))%Mod; if(j>=2) f[i+1][j-2][k+2]=(f[i+1][j-2][k+2]+f[i][j][k]*(j*(j-1)/2))%Mod; } LL ans=0; for(int j=0;j<=m;++j) for(int k=0;k<=m-j;++k) ans=(ans+f[n][j][k])%Mod; printf("%lld",ans); return 0; }